Agenda for today 1. Descriptive Data Analysis 2. Graphics XploRe - - PowerPoint PPT Presentation

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Agenda for today

• 1. Descriptive Data Analysis
• 2. Graphics

XploRe

Descriptive Data Analysis 1-2

Prerequisites

1

library("xplore")

2

library("stats")

3

setenv(" outputstringformat ","%s")

Avoid quotes in text output.

XploRe

Descriptive Data Analysis 1-3

Descriptive Data Analysis

⊡ typically the first part of statistical modeling ⊡ evaluation of data ⊡ All routines from libraries xplore (basic routines) and stats (basic statistical methods)

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Descriptive Data Analysis 1-4

Data Matrices

⊡ z = #(x1, x2, . . . , xn) creates a column vector z from scalar numbers x1, x2, . . . , xn ⊡ z = x|y concatenates two arrays x and y rowwise ⊡ z = x ∼ y concatenates two arrays x and y columnwise

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Descriptive Data Analysis 1-5

Reading Data

1 x = read("file") 2

reads numeric data from file.dat

3 x = readm("file") 4

reads mixed text and numeric data from file.dat XploRe

Descriptive Data Analysis 1-6

Dimensions of a Dataset

1 d = dim(x) 2

shows the dimension of an array x

3 n = rows(x) 4

shows the number of rows of an array x

5 p = cols(x) 6

shows the number of columns of an array x

7 y = x[i,j] or y = x[i,] or y = x[,j] 8

extracts element i,j or row i or column j from x

9 z = x[k:l,m:n] 10

extracts rows k to l and columns m to n XploRe

Descriptive Data Analysis 1-7

Minimum and Maximum

1 mx = min(x {,d}) 2

computes the minimum of an array x, optionally with respect to dimension d

3 mx = max(x {,d}) 4

computes the maximum of an array x, optionally with respect to dimension d XploRe

Descriptive Data Analysis 1-8

Mean, Variance and other Moments

1 mx = mean(x {,d}) 2

computes the mean of an array x, optionally with respect to dimension d

3 vx = var(x {,d}) 4

computes the variance of an array x, optionally with respect to dimension d

5 kx = kurtosis(x) 6

computes the (columnwise) kurtosis of an array x

7 sx = skewness(x) 8

computes the (columnwise) skewness of an array x XploRe

Descriptive Data Analysis 1-9

Median and Quantiles

1 mx = median(x) 2

computes the (columnwise) median of an array x

3 qx = quantile(x, alpha) 4

computes the (columnwise) quantile of an array x at level alpha XploRe

Descriptive Data Analysis 1-10

Covariance and Correlation

1 cx = cov(x) 2

computes the covariance matrix of a data matrix x

3 rx = corr(x) 4

computes the correlation matrix of a data matrix x XploRe

Descriptive Data Analysis 1-11

Categorical Data

1 {xr , r} = discrete(x {,y}) 2

reduces a matrix to its distinct rows

3

and gives the number of replications of each row

4

in the

• riginal

data set XploRe

Descriptive Data Analysis 1-12

Categorical Data

1 setenv(" outputstringformat ","%s") 2

library("xplore")

3

library("stats")

4 earn=read("cps85") 5 earn=earn [ ,1|2|5|8|10|11|12] 6 {cat ,freq}=discrete(earn [,3]) 7 cat 8 freq

XploRe

Descriptive Data Analysis 1-13

Missing Data

1 nx = countNaN(x) 2

counts missing values in an array x

3 nx = countNotNumber (x) 4

counts missing and infinite values in an array x

5 ix = isNaN (x) 6

determines whether the elements of an array x are missing values

7 ix = isInf (x) 8

determines whether the elements of an array x are infinite values XploRe

Descriptive Data Analysis 1-14

Missing Data

1 ix = isNumber (x) 2

determines whether the elements of an array x are regular numeric values

3 y = paf(x, i) 4

deletes all rows of x for which the corresponding element of i equals 0

5 y = replace(x, w, b) 6

replaces all elements of x which equal w by the value b XploRe

Summarizing Information 2-15

Summarizing Information

1 s = summarize(x {,xvars }) 2

computes a short summary of descriptive statistics

3 s = fivenum(x {,xvars }) 4

computes the five number summary for each column

• f a matrix x

5 s = descriptive(x {,xvars }) 6

computes detailed descriptive statistics for each column of a matrix x

• ptionally a vector of variable names xvars can be given

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Summarizing Information 2-16

Summarizing Metric Data

1 s = summarize(x {,xvars }) 2

computes a short summary of descriptive statistics

3 s = fivenum(x {,xvars }) 4

computes the five number summary for each column

• f a matrix x

5 s = descriptive(x {,xvars }) 6

computes detailed descriptive statistics for each column of a matrix x

• ptionally a vector of variable names xvars can be given

XploRe

Summarizing Information 2-17

Summarizing Categorical Data

1 s = frequency(x {, xvars {, outwidth }}) 2

computes frequency table for each column of a matrix x

3 s = crosstable(x{,xvars }) 4

computes pairwise cross tables from all columns

5

computes the result of a $ \chi^2$ independence test

• ptionally a vector of variable names xvars can be given

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Graphics 3-18

Graphics Overview

⊡ the graphical tools (high-level): plot* ⊡ the graphical primitives (low-level) gr* ⊡ the graphical commands

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Graphics 3-19

Basic Plotting

1 plot(x1 {, x2 { ,...{x5 }}}) 2

plots the data sets x1 ,...,x5

3 line(x1 {, x2 {, ... {x5 }}}) 4

plots the lines sets x1 , ..., x5

5 y = setmask (x, opt1 {, opt2 {, ... {opt9 }}}) 6

modifies a data set for plotting

7 disp = createdisplay (r,c) 8

creates a display disp

9 show(disp , i, j, x1 {, x2 {, ... {, xn }}}) 10

plots the data sets x1 , ..., xn in the display disp d XploRe

Graphics 3-20

Basic Plotting

1

library ("plot") ; loads library plot

2 data = read ("bostonh")

; reads Boston Housing data

3 x = data [ ,13:14]

; selects columns 13 and 14

4 plot(x)

; plots data set XploRe

Graphics 3-21

Example plot

10 20 30 X 10 20 30 40 50 Y

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Graphics 3-22

Basic Plotting

1

library("plot") ; loads library plot

2 xmin = 0

; grid minimum

3 xmax = 2*pi

; grid maximum

4 n

= 100 ; number of grid points

5 x = xmin + (xmax -xmin)/(n-1) .* (0:n-1) 6 ; generates

grid

7 y = sin(x)

; computes sin(x)

8 plot(x~y)

; plots data set XploRe

Graphics 3-23

Example plot

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Graphics 3-24

Multiple Plots

1

library("plot")

2

xmin = 0

3

xmax = 2*pi

4

n = 100

5

x = xmin + (xmax -xmin)/(n-1) .* (0:n-1)

6

y1 = sin(x)

7

y2 = sin (3.*x)

8

y3 = sin (6.*x)

9

plot(x~y1 , x~y2 , x~y3) XploRe

Graphics 3-25

Example plot

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Colors

1

library("plot")

2

xmin = 0

3

xmax = 2*pi

4

n = 100

5

x = xmin + (xmax -xmin)/(n-1) .* (0:n-1)

6

y1 = sin(x)

7

y2 = sin (3.*x)

8

y3 = sin (6.*x)

9

z1 = setmask(x~y1 , "red")

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z2 = setmask(x~y2 , "green")

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z3 = setmask(x~y3 , "blue")

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plot(z1 , z2 , z3)

Graphics 3-27

Example plot

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Graphics 3-28

Plotting Lines

1

library("plot")

2

xmin = 0

3

xmax = 2*pi

4

n = 100

5

x = xmin + (xmax -xmin)/(n-1) .* (0:n-1)

6

y1 = sin(x)

7

y2 = sin (3.*x)

8

y3 = sin (6.*x)

9

line(x~y1 , x~y2 , x~y3) XploRe

Graphics 3-29

Example plot

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Graphics 3-30

Lines and Colors

1

library("plot")

2

xmin = 0

3

xmax = 2*pi

4

n = 100

5

x = xmin + (xmax -xmin)/(n-1) .* (0:n-1)

6

y1 = sin(x)

7

y2 = sin (3.*x)

8

y3 = sin (6.*x)

9

plot(x~y1 , x~y2 , x~y3)

10

z1 = setmask(x~y1 , "line", "red")

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z2 = setmask(x~y2 , "line", "green")

12

z3 = setmask(x~y3 , "line", "blue")

13

plot(z1 , z2 , z3) XploRe

Graphics 3-31

Example plot

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Graphics 3-32

Multiple Plots

1 disp = createdisplay (rownum , colnum) 2 3 show(disp ,<row>,<col>, what)

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